Emerging time-resolved volumetric PIV techniques have made simultaneous measurements of velocity and pressure fields possible. Yet, in many experimental setups, satisfying the spatial and temporal resolution requirements is a challenge. To improve the quality of sparse and noisy data, this paper introduces a constrained cost minimization (CCM) technique, which interpolates unstructured particle tracks to obtain the velocity, velocity gradients, material acceleration, hence the pressure, on a Eulerian grid. This technique incorporates physical constraints, such as a divergence-free velocity field and curl-free pressure gradients. The performance is evaluated using synthetic particle tracks for an unsteady double gyre and direct numerical simulations data for a turbulent channel flow, with varying particle concentrations and added errors. The errors in pressure, calculated using omni-directional integration, and correlations with the original data are compared to those obtained using the singular value decomposition (SVD) interpolation technique. The CCM errors are mostly lower, and the correlation is higher and less sensitive to particle sparsity and added errors compared to those of SVD. The synthetic particle traces are also projected onto four planar images to evaluate the performance of the new procedure together with shake-the-box (STB) particle tracking. A comparison of pressure spectra and correlation with the original data show very good agreement for the CCM method. Hence, CCM appears to be an effective method for improving the interpolation of sparse data. Sample experimental data obtained in the shear layer behind a backward-facing step demonstrate the application of STB and CCM to resolve the pressure field in coherent vortex structures.

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中文翻译：

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使用受约束的成本最小化从嘈杂的稀疏粒子轨道重构速度和压力

新兴的时间分辨体积PIV技术使​​得同时测量速度和压力场成为可能。然而，在许多实验装置中，满足空间和时间分辨率要求是一个挑战。为了提高稀疏和嘈杂数据的质量，本文引入了一种约束成本最小化（CCM）技术，该技术对非结构化的粒子轨迹进行插值以获得欧拉网格上的速度，速度梯度，材料加速度以及压力。该技术结合了物理约束，例如无散度的速度场和无卷曲的压力梯度。使用具有不稳定双回转的合成粒子轨迹和湍流通道流动的直接数值模拟数据（具有变化的粒子浓度和增加的误差）来评估性能。将使用全向积分计算的压力误差以及与原始数据的相关性与使用奇异值分解（SVD）插值技术获得的误差进行比较。与SVD相比，CCM误差大多较低，并且相关性较高，并且对粒子稀疏性和附加误差不敏感。合成的颗粒痕迹也被投影到四个平面图像上，以评估新程序的性能以及“摇篮”（STB）颗粒跟踪。压力谱图和相关性与原始数据的比较表明，CCM方法具有很好的一致性。因此，CCM似乎是一种改进稀疏数据插值的有效方法。

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